## Real AnalysisThis is the classic introductory graduate text. Heart of the book is measure theory and Lebesque integration. |

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### Contents

Prologue to the Student | 1 |

The Real Number System | 31 |

The Lebesgue Integral | 75 |

Copyright | |

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a-algebra a-finite absolutely continuous axiom Baire sets Banach space Borel measure Borel sets called Cauchy sequence closed set cluster point compact Hausdorff space compact set complete metric space continuous function continuous map continuous real-valued function Convergence Theorem Corollary countable collection cr-algebra cr-finite definition denote dense element equicontinuous finite measure finite number following proposition func function defined function f given Hausdorff space Hence Hint homeomorphism inequality inner regular integrable function isomorphic Lebesgue measure Lemma Let f Let G locally compact Hausdorff measurable function measurable sets measure space measure zero monotone natural numbers nonempty nonnegative measurable function one-to-one open covering open intervals open set open subset outer measure point of closure Problem Proof Prove Proposition satisfies sequence of measurable set function set of measure Show simple functions subspace tion topological space topologically equicontinuous unique